Have seen your previous posts, but thought the suggestions there would have solved problem. Have you done the following:
1) Checked for vacuum leaks? (Remove oil filler cap at warm idle. Engine should stumble and/or die. If not, you have a vacuum leak).
2) Undone, cleaned, recrimped and reattached EVERY electrical connection under the hood?
3) Checked that you have a good, topped up battery, again with clean, non-corroded connectors?
4) Made sure all fuses (including fusable links) are making good, clean contact?
5) Checked the air bypass valve? (Or is that the same as the air regulator — might be). It's easy, though: take it off, hook 12V to the two connectors and watch the little door close in about a minute. If it doesn't, or if you can't look through it (door stuck closed), the valve is no good, which could cause backfire through AFM.
6) Made sure you're running premium gas?
7) Not done anything immediately previous to this problem starting? If you have, go back and look for wires and vacuum fittings you might have mistakenly dislodged.
8) Made sure you are running NGK spark plugs?
9) Made sure timing is correct?
And just to make sure we're all on the same page, the car runs fine once it does warm up, correct? JUST in the transition period when it's on the cold-start cycle is when you're having the problem, right?
If the car is running all right when warmed up, I doubt if your problem is in the AFM, distributor or anywhere else but the cold-start system. (Although I suspect backfiring could "injure" the AFM.) What I would do at this point is look up the problem in the Factory Service Manual and start following their excellent trouble-shooting 'trees' until the problem was isolated and solved. If you don't have an FSM, well I would suggest getting one — unless you don't mind tearing your hair out and spending lots of money you probably didn't have to. If for some reason you can't get an FSM, I would start by vigorously jiggling wires and connectors that are part of the cold-start system when the car is warming up. You'd be surprised how often this reveals a problem. Jiggle them when it's warm, too. Failing that, disconnect the cold start system entirely. Unless it's freezing cold, the engine should start without that stuff hooked up (mine does), it will just run ragged until warm. However, if it's still backfiring when cold start stuff is not hooked up, then you've eliminated that system as part of the problem. At that point, I might try swapping another ECU (from a wrecking yard car, quit buying so much new stuff) and see if that makes any difference.
My basic philosophy with this stuff is do the quick, cheap stuff first and work your way up. I have a whole drawer full of sensors and misc fittings I've pulled of motors at the junkyard and I think the whole drawerful cost $15 or $20 tops. I try to test most of them (using specs in the Factory Manual, hint, hint) when I get them home, and just throw out the ones that don't pass. I have 5 or 6 good air bypass valves now, for example. They were like a buck or two each, not $60 or whatever MSA gets for new ones these days. If I was really into building the best Z I could, I'd test out components using spares to find the problem. And only THEN, when I was SURE that I'd solved it, would I ever give these robbers top dollar for a shiney new sensor. Just my 2¢.